Thermodynamic Efficiency

"Gasification is more efficient thermodynamically than direct combustion of the fuel source as the gas can be combusted at higher temperatures, resulting in higher thermodynamic efficiencies as defined by Carnot's rule"

Now, this statement is true because you can indeed combust the gas at higher temperatures than the fuel directly, meaning that the hot reservoir temperature is greater (η=1-(Tc/Th)).

However, how would you prove this statement in a more fundamental way? How do you calculate or prove that the gas is able to be combusted at higher temperatures than the fuel itself?

In addition, how would you prove mathematically that one fuel (say a syngas rich in H2 compared to a poorer heating quality syngas) can be combusted at higher temperatures than another, resulting in an improved thermodynamic upper limit efficiency defined by Carnot? Is it simply a case of calculating the heat of combustion?

Gasification removes the ashes out of the fuel.
Therefore the produced gas ought to have a higher flame temperature.

This is likely what happens, but it does not need to always be the case.
It could also happen that a solid combustible part of the fuel remains ungasified and that the gasified part has a low heat value. For example, if CO is the gas produced it might well have a lower heat value than the un-converted carbon.

But generally, it can happen that gasification increases heat value.
This is then just a purification of the fuel.

Ask yourself, how does a solid, such as wood burn?
is it the solid burning or is it really the wood being heated up and being "gasified", and the gases burning. To gasify the wood, heat has to be added to the solid fuel to raise its temperature. One can do that previous to the combustion process or during, in which case the flame temperature will be higher.

"Gasification is more efficient thermodynamically than direct combustion of the fuel source as the gas can be combusted at higher temperatures, resulting in higher thermodynamic efficiencies as defined by Carnot's rule"

Click to expand...

So if your statement splits the process into 2 phases - the gasification of the wood and the combustion of the gas, then certainly eliminating the first phase and disregarding the heat value necessary to gasify the solid wood, then sure, it does look more efficient for the end user. Overall, there is no free lunch so to speak though.

Note that gasification requires energy and also leaves a degraded waste.
Therefore, overall, there cannot be an increase of efficiency.
It is just that the gasified fuel offers a better efficiency.
The available work from the initial fuel is not increased.